Communicating sequential processes
Communicating sequential processes
Programming language syntax and semantics
Programming language syntax and semantics
An axiomatic basis for computer programming
Communications of the ACM
Problem frames: analyzing and structuring software development problems
Problem frames: analyzing and structuring software development problems
Algebraic Semantics of Imperative Programs
Algebraic Semantics of Imperative Programs
Computer Architecture: A Quantitative Approach
Computer Architecture: A Quantitative Approach
Java(TM) Language Specification, The (3rd Edition) (Java (Addison-Wesley))
Java(TM) Language Specification, The (3rd Edition) (Java (Addison-Wesley))
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This paper analyses the interpretation of mathematical entities in the formalisations of languages. Four case studies are considered, covering both denotational and axiomatic approaches. We argue that the usual interpretation consists of direct statements about the language concepts and, occasionally, about the real world; some problems of this approach are discussed. Applying results from philosophical studies into the structure of scientific theories, we propose an alternative interpretation of mathematical entities as statements defining constructed concepts, which can be employed in turn as theoretical models of the language concepts and the world. Though this approach requires us to write hypotheses claiming some similarity between the models and the represented subjects, we reason that it is more adequate for formalising certain languages.